Method and apparatus for data transmission using multiple transmit antennas

ABSTRACT

A method and apparatus for increasing the data rate and providing antenna diversity using multiple transmit antennas utilize a set of bits of a digital signal to generate a codeword. Delay elements may be provided in antenna output channels, or, with suitable code construction, delay may be omitted. n signals represent n symbols of a codeword are transmitted with n different transmit antennas. At the receiver, the noisy received sequence is decoded. The parallel transmission and channel coding enables an increase the data rate over previous techniques, and recovery even under fading conditions. The channel coding may be concatenated with error correction codes under appropriate conditions.

This application is a continuation of U.S. patent application Ser. No.11/974,395, filed Oct. 12, 2007, which is currently allowed and is acontinuation of U.S. patent application Ser. No. 11/115,447, filed Apr.27, 2005, now U.S. Pat. No. 7,298,794; which is a continuation of U.S.patent application Ser. No. 09/545,791, filed Apr. 7, 2000, now U.S.Pat. No. 6,889,355, which is a continuation of U.S. patent applicationSer. No. 08/847,635 filed Apr. 25, 1997, now U.S. Pat. No. 6,115,427,which claims priority to U.S. Provisional Application Ser. No.60/017,046 filed Apr. 26, 1996 and to U.S. Provisional Application Ser.No. 60/030,571 filed Nov. 7, 1996, all of which are herein incorporatedby reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of Invention

The present invention relates generally to the field of communicationssystems, and particularly to the field of wireless communications, suchas cellular radio.

2. Description of Related Art

Antenna diversity is a technique used in communication system, includingmobile cellular radio, to reduce the effects of multi-path distortionfading. Antenna diversity may be obtained by providing a receiver withtwo or more (n≧2) antennas. These n antennas, when, properly positioned,imply n channels which suffer fading in different manners. When onechannel is in deep fade—that is, suffering severe amplitude and phaseloss due to the destructive effects of multi-path interference, anotherof these channels is unlikely to be suffering from the same effectsimultaneously. The redundancy provided by these independent channelsenables a receiver to often avoid the detrimental effects of fading.

Alternatively, antenna diversity benefit can be provided to a mobilereceiver by providing multiple transmitting antennas at a base ortransmitting station, rather than at the receiver. The receiver cantherefore use a single antenna, saving cost and complexity at that sideof the transmission chain.

Multiple transmit antennas can be provided at the base station in avariety of way. A schematic diagram of certain possible known techniquesis illustrated in FIG. 1. Perhaps most simply, as schematicallyillustrated in FIG. 1( a) two antennas can be provided at the outputstage, and the information signal d_(k) can be switched between twomatched antenna elements, without overlap in time or frequency. Ofcourse this has the drawback that the transmitter requires feedback fromthe receiver about the channels corresponding to each transmit antenna.This scheme does not perform well when the channel is rapidly changing.

In a variant described in U.S. Pat. No. 5,479,448 and schematicallyillustrated in FIG. 1( b), the above mentioned drawbacks of switchdiversity are removed by using a channel code to provide diversitybenefit. Maximum diversity is upper-bounded by the number of antennaelements at the base station, and is equal to the minimum Hammingdistance of the channel code used, provided that the receiver isequipped with one antenna. The system described in that patent isapplicable to both FDD (frequency division duplex) and TDD (timedivision duplex)—based systems.

Illustrative embodiments of the system of U.S. Pat. No. 5,479,448comprise a base station which employs a channel code of length n≧2symbols (n being the number of antennas used by the transmitter), and aminimum Hamming distance 2≧d_(min)≧n. This channel code is used toencode a group of k information bits. The n antennas of the base stationtransmitter are separated by a few wavelengths, as is conventional toprovide the diversity reception with the n antennas. The channel codesymbol c_(i) is transmitted with the i^(th) antenna to represent these kbits. At a receiver, a conventional maximum likelihood channel codedecoder provides a diversity advantage of d_(min).

In the preferred embodiment of U.S. Pat. No. 5,479,448, the transmittedsignals from different antennas are separated in time. This results indata rate reduction, sacrificing bandwidth. The reduction in data rateis equal to the number of antennas (or length of the code).

Transmit bandwidth can be improved over the diversity arrangement ofFIG. 1( b), by splitting the information signal into two paths to thetwo antennas, the second of which has a delay element or tap asdisclosed in A. Wittneben, “Base Station Modulation Diversity forDigital SIMULCAST,” 41^(st) IEEE Vehicular Technology Society ConferenceProceedings, pp. 848-853 and shown in FIG. 1( c). The signal appearingat B at any given instant of time is therefore the same signal asappeared at antenna A the preceding instant of time. The two signals aretransmitted simultaneously, reconstructed at the receiving station, andprocessed to isolate the desired information signal.

SUMMARY OF THE INVENTION

The invention improving on these and other communication techniques inone aspect relates to a system and method for data transmission usingmultiple transmit antennas.

The invention in one aspect relates to the system and method for datatransmission which increases effective utilization of available channelbandwidth, without great increases in transmitter or receiver complexityor cost. The invention in another aspect relates to a system and methodfor data transmission which utilizes channel-codes to transmit data,reducing the chance of error and increasing reception robustness.

The invention in another aspect relates to a system and method for datatransmission which can include concatenated error correcting codes, evenfurther increasing BER and other transmission performance.

The invention in another aspect relates to a system and method for datatransmission which can include multilevel coding, and decreases decodingcomplexity.

The invention in another aspect relates to a system and method for datatransmission which preserves diversity benefit from multiple antennaarrangements, under a wide range of conditions.

In the present invention, among other advantages the time separationdescribed in U.S. Pat. No. 5,749,448 is removed, and coded data istransmitted in parallel, simultaneously from different transmitantennas, with or without delay. Increased data rate as well asdiversity are achieved.

By way of comparison, the codes described in U.S. Pat. No. 5,749,448(col. 6, lines 21-29; col. 7, lines 35-44 and 63-67; col. 8, lines 1-16)provide a diversity 2 using 2 transmit antennas and 1 receive antenna.The bandwidth efficiencies for these disclosed codes are 1 bit/symbol,1.5 bits/symbol and 2 bits/symbol respectively.

Using the present invention as described below, applying the same codesbut a new transmission arrangement, the bandwidth efficiency doubles to2, 3 and 4 bits/symbol respectively. Moreover, in another embodiment ofthe present invention when coding is done taking into account diversityand other criteria, no delay element on the antenna line is necessary toimplement the invention and further coding gain is obtained.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1( a), 1(b) and 1(c) illustrate a schematic diagram of certainprior approaches to multiple transmit antennas at base stations;

FIGS. 2( a) and 2(b) illustrate a schematic block diagram of first andsecond embodiments of multiple transmit antenna base stations, accordingto the invention;

FIG. 3 illustrates a schematic block diagram of a wireless communicationsystem constructed according to the illustrative first embodiment of theinvention;

FIG. 4 illustrates signal constellations used in implementations of theinvention;

FIG. 5 illustrates a schematic block diagram of a receiver constructedin conjunction with the first illustrative embodiment of the invention;

FIG. 6 illustrates a schematic block diagram of decoding circuitry usedin the receiver constructed according to the first illustrativeembodiment of the invention;

FIG. 7 illustrates a schematic block diagram of a receiver like thatshown in FIG. 5, but adapted to use two antenna elements;

FIG. 8 illustrates a schematic block diagram of a wireless communicationsystem constructed according to a second illustrative embodiment of theinvention;

FIG. 9 illustrates a 4-PSK code, used in implementation of the secondillustrative embodiment of the invention;

FIG. 10 illustrates a schematic block diagram of decoding circuitry usedin a receiver constructed according to the second illustrativeembodiment of the invention;

FIG. 11 illustrates an 8-PSK code, used in implementation of the secondillustrative embodiment of the invention;

FIG. 12A-12B collectively illustrate a 4-PSK code with 8 and 16 states,used in implementation of the second illustrative embodiment of theinvention;

FIG. 13 illustrates a 4-PSK code with 32 states, used in implementationof the second illustrative embodiment of the invention;

FIG. 14 illustrates a 2-Space-Time QAM code with 16 and 16 states, usedin implementation of the second illustrative embodiment of theinvention.

FIG. 15 illustrates data demonstrating transmission performance oftransmission according to the second illustrative embodiment of theinvention; and

FIG. 16 illustrates a time slot structure related to channel probingtechniques used in connection with the invention;

FIG. 17 illustrates a schematic diagram of a transmitter that employsspace-time coding with 2 transmit antennas;

FIG. 18 illustrates a schematic diagram of the receiver with space-timevector Viterbi decoder;

FIG. 19 illustrates the frame-error-rate performance of the basic modemstructure;

FIG. 20 shows the estimated distribution of the number of symbol errorsper frame at Doppler frequency 170 Hz;

FIG. 21 illustrates a schematic diagram for the transmitter withconcatenated space-time coding according to a third illustrativeembodiment of the invention;

FIG. 22 illustrates a schematic diagram for the receiver with space-timevector Viterbi decoder concatenated with a Reed-Solomon decoderaccording to the third illustrative embodiment;

FIG. 23 illustrates the performance of the concatenated space-time codeof the third illustrative embodiment of the invention;

FIG. 24 describes set partitioning of a 16 QAM constellation to be usedin an example of multi-level space-time codes according to the fourthillustrative embodiment of the invention;

FIG. 25 describes example of encoders for different levels ofmulti-level space-time code;

FIG. 26 describes an equivalent space-time code for an example of amulti-level space-time code constructed according to the fourthillustrative embodiment of the invention; and

FIGS. 27( a) and 27(b) respectively illustrate smart greedy codesconstructed using the BPSK and 4-PSK constellations, according to afifth illustrative embodiment of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS A. Incorporation byReference

Various concepts of digital signal processing referred to in thisapplication are well known in, for example, the digital communicationand other arts, and thus they need not be described in detail herein.These concepts are described for instance in U.S. Pat. No. 4,457,004,issued Jun. 26, 1984 to A. Gersho et al.; U.S. Pat. No. 4,489,418,issued Dec. 18, 2984 to J. E. Mazo; U.S. Pat. No. 4,520,490, issued May28, 1985 to L. Wei; U.S. Pat. No. 4,597,090, issued Jun. 24, 1986 to G.D. Formey, Jr.; U.S. Pat. No. 5,029,185 issued Jul. 2, 1991 to L. Wei;in A. Wittneben, “Base Station Modulation Diversity for DigitalSIMULCAST,” 41^(st) IEEE Vehicular Technology Society ConferenceProceedings, pp. 848-853; and U.S. Pat. No. 5,479,448 to Seshadri, allof which are incorporated by reference.

B. Illustrative Hardware used in Embodiments

For clarity of explanation, illustrative embodiments of the presentinvention are presented as comprising individual functional blocks. Asknown in the art, the functions these blocks represent may be providedthrough the use of either shared or dedicated hardware (processors),including, but not limited to, hardware capable of executing software.Illustrative embodiments may comprise digital signal processor (DSP)hardware, and software performing the operations discussed below. Verylarge scale integration (VLSI) hardware embodiments of the presentinvention, as well as hybrid DSP/VLSI embodiments, may also beconstructed.

C. Introduction to Illustrative Embodiments

The central idea of conventional antenna diversity reception is thatwith high probability, a signal received at different antennas undergoesfading at different moments in time. Thus, a receiver can combine orselect different receive signals to reconstruct the transmitted signalwith little distortion.

The present invention provides the benefit of diversity by takingadvantage of multiple antennas at a transmitter, with or without delay.A first illustrative embodiment shown in FIGS. 2( a) and 3 maps theinformation sequence of length M₁ to a two code sequence of length M₂.In particular every group of k input bits (assume k divides M₁) aremapped to first and second code symbols. The two code symbols are usedto form two code sequences where each sequence is of length M₁/k=M₂where the first code sequence is comprised of the first code sequence iscomprised of the second code symbol. These two code sequences are thenused to phase modulate a carrier using conventional phase shift keying,as is well known in the art, and in that process two modulated signalsare generated. Alternatively, quadrature amplitude modulation, or anyother modulation scheme can be used.

The two modulated signals are then transmitted using two transmitantennas. In the first illustrative embodiment, a timing offset of onesymbol interval (delay element or tap, of period T) is introducedbetween the two signals. The receiver receives a sum of faded versionsof the transmitted signals from the two antennas, perturbed by noise. Inthe second illustrative embodiment, the use of a delay in one of theantenna channels is eliminated.

Because the two coded signals are transmitted simultaneously, nobandwidth penalty is incurred. However intersymbol interference iscreated which is resolved at the receiver using maximum likelihoodsequence detection or other techniques that are known in the art. Asnoted, the introduction of delay to provide diversity is known in theart. However the use of coding as an integral part of the delaydiversity arrangement is not known, nor is elimination of any delayelement using codes which adhere to diversity and other criteria. Priorto proceeding with a description of the illustrative embodiments of thepresent invention, concepts related to a channel model for the firstillustrative embodiment and embodiment error performance will bepresented.

D. Channel Model Transmission Format: Analysis in First IllustrativeEmbodiment

The overall transmission environment in which the first illustrativeembodiment of the invention operates may be viewed as comprising ndistinct channels, each illustratively undergoing independent slow(static) Rayleigh fading (it should be understood that the principles ofthe present invention are applicable to other classes of fading channelsas well). The impulse response for the i^(th) channel is given byh ₁(t)=α₁δ(t)e ^(jω) ⁰ ^(t),1≦i≦N  (1)

where ω₀ is the angular carrier frequency and z_(i) is the staticcomplex fade value whose phase is a random variable that is uniformlydistributed over [−π, π), and whose magnitude is Rayleigh distributedwithP(|α₁ |e ^(−|α) ¹ |² ,z ₁≧0  (2)

The information sequence I is grouped into sub-sequences of kinformation bits,

$I = {( {\underset{\underset{1{st}\mspace{14mu}{sub}\text{-}{sequence}}{︸}}{I_{0}^{1},I_{1}^{1},I_{2}^{1},\ldots\mspace{14mu},I_{k - 1}^{1}},\underset{\underset{2{nd}\mspace{14mu}{sub}\text{-}{sequence}}{︸}}{I_{0}^{2},\ldots\mspace{14mu},I_{k - 1}^{2}},\ldots}\mspace{14mu} ).}$

where the superscript is the sub-sequence number. Each sub-sequence ismapped into n channel symbols of the channel constellation using acannel code. Some of the illustrative signal constellations are shown inFIG. 4. The signal constellation mapped code sequence is

$c = {( {\underset{\begin{matrix}{{code}\mspace{14mu}{sequence}\mspace{14mu}{for}} \\{1{st}\mspace{14mu}{sub}\text{-}{sequence}}\end{matrix}}{\underset{︸}{c_{0}^{1},\ldots\mspace{14mu},c_{n - 1}^{1}}},\underset{\begin{matrix}{{code}\mspace{14mu}{sequence}\mspace{14mu}{for}} \\{2{nd}\mspace{14mu}{sub}\text{-}{sequence}}\end{matrix}}{\underset{︸}{c_{0}^{2},\ldots\mspace{14mu},c_{n - 1}^{2}}},\ldots}\mspace{14mu} ).}$

Hence each element c_(i) ^(j) is a point belonging to a signalconstellation. The code sequence is arranged in a matrix as shown below

$\begin{bmatrix}c_{0}^{1} & c_{0}^{2} & c_{0}^{3} & \ldots \\c_{1}^{1} & c_{1}^{2} & c_{1}^{3} & \; \\\vdots & \; & \; & \; \\c_{n - 1}^{1} & c_{n - 1}^{2} & c_{n - 1}^{3} & \ldots\end{bmatrix}.$

The first row of the matrix is pulse shaped using square-root Nyquistfilter (p(t), modulated and transmitted using antenna 1. The second rowof the matrix is pulse shaped using square-root Nyquist filter p(t−T)(p(t) delayed by one symbol interval). The i^(th) row of the matrix istransmitted using square root Nyquist filter p(t−(i−1)T) (p(t) delayedby (i−1) symbol intervals). At the receiver, the received signal,following demodulation, receiver filtering and sampling as is well knownin the art, is given byr _(i)=α₀ c ₀ ^(i)+α₁ c ₁ ^(i−1)+α₂ c ₂ ^(i−2)+ . . . +α_(n−j) c _(n−j)^(i−(n−1))+η_(i)

where η_(i) is the extraneous noise which is modeled as addictive whiteGaussian.

Decoding is done in a conventional manner using maximum likelihooddecoding techniques or suboptimum variants thereof, which are well knownin the art.

E. First Illustrative Embodiment

FIG. 3 presents an illustrative apparatus of a digital wirelesscommunication system transmitter according to a first illustrativeembodiment of the present invention. The transmitter receives an analogspeech signal from speech signal source 101, and processes this signalfor transmission on antennas 116 a, b. The transmitter comprises asource encoder 104, a channel encoder 106, constellation mappers 108 a,b, temporary storage buffers 110 a, b, pulse shapers 112 a and b, themodulators 114 a, b. Power amplification associated with thetransmission of radio signals has been omitted from FIG. 3 for clarity.

The speech signal source 101 provides an analog speech signal to beencoded and transmitted for instance to a mobile receiver. This speechsignal is converted to a digital signal by conventionalanalog-to-digital conversion by source encoder 104. Source encoder 104provides a digital signal representative of the analog speech signal asoutput to channel encoder 106. Source encoder 104 may be realized withany of the conventional speech encoders.

The channel encoder 106 receives the PCM (Pulse Code Modulated) digitalsignal comprising a plurality of bits from the source encoder 104.Channel encoder 106 codes the PCM digital signal using a conventionalchannel code. Any channel code may be employed for this purpose, as longas it is appropriately constructed.

The code constructed for the first illustrative embodiment of thepresent invention assumes that the number of antennas at the basestation is two. The following illustrative code of length n=2 complexsymbols (2 symbols×2 components (in-phase and quadrature) per symbolequals 4 dimensions (4-D)), has a minimum Hamming distance d_(min)=2.

Channel Code Information Bits Symbol 1 Symbol 2 00 0 0 01 1 2 11 2 1 103 3

Using this code, encoder 106 codes two information bits at a time togenerate one of four codewords. Each generated codeword comprises twosymbols (see columns labeled Symbol 1 and Symbol 2, above). Each symbolbelongs to the 4-PSK constellation presented in FIG. 4( a). Thus, acoding rate of one information bit per code symbol is provided by thiscode. Symbol 1 is transmitted with antenna 116 a and symbol 2 withantenna 116 b, as discussed below.

The first symbol of each codeword generated by encoder 106 is providedas input to constellation mapper 108 a, and the second symbol of thecodeword is provided to mapper 108 b.

Constellation mappers 108 a, b produce a complex valued outputcorresponding to a symbol received from encoder 106. The real part ofthis output determines an in-phase component of a modulated signaltransmitted at antennas 116 a,b. Similarly, the imaginary part of theoutput determines a quadrature component of the modulated signal. Theconstellation mapper 108 a,b are conventional mappers known in the art.They may be realized as a look-up table or as a straightforwardcombination of logic elements. Mappers 108 a,b operate on the first andsecond symbol of each received codeword, respectively, and providecomplex valued output to buffers 110 a and b.

Buffers 110 a and b provide temporary storage for the complex valuesreceived form mappers 108 a, b, and illustratively store 100 of suchvalues. The complex entries in buffer 110 a are pulse shaped usingconventional square-root Nyquist transmit filter (see 112 a) while thosein buffer 110 b are pulse shaped using the same square-root Nyquisttransmit filter but whose impulse response is delayed by one symbolinterval (see 112 b). The pulse shaped outputs are then modulated bymodulators 114 a and 114 b and transmitted using antennas 116 a and 116b. Additional filtering and power amplification stages are not shown forclarity.

F. Further Channel Codes for First Illustrative Embodiment

The first embodiment described above may employ other channel codes thanthe one first developed, to enhance coding efficiency. For example, thefollowing code length 2, d_(min)=2, is formed from an 8-PSKconstellation shown in FIG. 4( b). This code has efficiency of 3bits/symbol:

Information Data Symbol 1 Symbol 2 000 0 0 001 1 5 011 2 2 111 3 7 100 44 101 5 1 110 6 6 111 7 3

A distinct pair of codewords differ in at least two positions.

In another coding implementation, a coding efficiency of 4.0 bits/symbolis provided. In order to achieve d_(min)=2 and stay within theconstraint that the block length of the code equal two, it is necessaryto have at least 16 codewords. Hence, 16-PSK (see FIG. 4( c)) is thesmallest constellation with which a diversity benefit of 2 can beprovided. The 4D-16 PSK code is shown below:

Information Data Symbol 1 Symbol 2 0000 0 0 0001 2 2 0010 4 4 0011 6 60100 8 8 0101 10 10 0110 12 12 0111 14 14 1000 1 7 1001 3 9 1010 5 111011 7 13 1100 9 15 1101 11 1 1110 13 3 1111 15 5

G. An Illustrative Decoder for Embodiments

FIG. 5 presents an illustrative receiver 300 according to the foregoingfirst illustrative embodiment of the present invention. Receiver 300receives transmitted signals from antenna 301, and produces analogspeech as output. Receiver 300 comprises an RF-to-baseband from end 305,receive buffer 307, channel decoder 310, and speech decoder 320.

The RF-to-baseband front end 305 provides conventional demodulatedoutput (e.g., received symbols) to the receive buffers 307. Front end305 includes, e.g., conventional RF to IF conversion, receive filtering,and tinting and carrier recovery circuits.

Receive buffer 307 store received symbols from front end 305. Buffer 307analogous to buffers 110 a, b of the illustrative transmitter describedin Section D and present in FIG. 3 except that since the receiverreceives a superposition of data in buffers 110 a, b only one buffer isneeded. Channel decoder 210 receives the demodulated symbol output frombuffer 307, and provides decoded information bits to speech decoder 320.The illustrative decoder 310 operates in accordance with the flowdiagram presented in FIG. 6.

As shown in FIG. 6, symbols from receive buffer 307 are used incomputing distances with all possible valid codewords stored in memories311 a, b. For example the first codeword from buffer 311 a takentogether with the first codeword from 311 b, but delayed by one unitsymbol interval are linearly combined with channel gains α₁ and α₂respectively. The distance between this combined output and the receivedsymbols in buffer 307 is computed. This is done for every codeword inbuffers 311 a and 311 b (see 312). The legal codeword pair is the onewhich most closely match the received sequence (see 313). The decodedcodeword pair is then mapped to a string of bits which comprises codedinformation (see 314). This exhaustive search can be implementedefficiently using the Viterbi algorithm or variants thereof, known topersons skilled in the art.

Speech decoder 320 is a conventional device providing a mapping ofdigital speech information to analog speech. Decoder 320 provides aninverse operation to source encoder 104 discussed above with respect toFIG. 5.

In light of the discussion above, it is to be understood that thediversity benefit of the present invention using one antenna may beenhanced by use of multiple receive antennas. This advantage may berealized by combination of a front end and receive buffer for eachreceiver antenna.

FIG. 7 presents an illustrative decoder in accordance with thisenhancement for two receiving antennas 301 a, b. As shown in the figure,received symbols from the first and second buffers associated with eachantenna are provided directly to channel decoder. These are processed ina manner similar to the one described above by the decoder and adecision on the transmitted signal is made.

H. Second Illustrative Embodiment: Introduction

In the present invention, the foregoing first illustrative embodiment ofthe invention and its coding implementations rely upon coding techniqueand a delay element in the antenna transmission line, to preservediversity and achieve additional coding gain over the simpler knowndelay diversity schemes. However, that illustrative embodiment can befurther improved by removing the restriction that delays be introducedbetween different coded streams.

In particular, in the second illustrative embodiment of the invention,the inventors derive criteria for maximizing the performance when ntransmit antennas are used to transmit n parallel data streams that arecreated by encoding information data with a channel code. In particular,it is shown that the code's performance is determined by the rank anddeterminant of certain matrices. These matrices in turn are constructedfrom codewords of the given channel code. These matrix based criteriaare used to design channel codes for high data rate wirelesscommunications. These codes are called space-time codes, and are easy toencode because they have a trellis structure. These codes can be easilydecoded using maximum likelihood sequence criterion. Examples of 4PSK,8PSK and 16QAM based codes are given that have been constructed foroperation with 2 and 4 transmit antennas. Performance results are shownto verify the performance.

I. Channel Model Transmission Format: Analysis for Second IllustrativeEmbodiment

The overall transmission channel in which the second illustrativeembodiment and its coding implementation operates may be viewed ascomprising n distinct channels, each illustratively undergoingindependent slow (static) Rayleigh or Rician fading (it should again beunderstood that the principles of the present invention and thisembodiment are applicable to other classes of fading channels as well),having impulse response, fade and other characteristics generally asdescribed above for the first illustrative embodiment.

J. Second Illustrative Embodiment

FIG. 8 presents a communication system constructed according to thesecond illustrative of the present invention. The system shown isgenerally similar to that of the first illustrative embodiment shown inFIG. 3, and elements in common with the previous embodiment are labeledwith similar numbers, including signal source 101, antennas 116 a, b,encoder 104 and channel encoder 106, and constellation mappers 108 a, b.It may be noted that pulse shaper 112 b′ in the second illustrativeembodiment is not constructed to apply a delay of T, but is the same aspulse shaper 112 a′.

The channel encoder 106 receives the PCM digital signal comprising aplurality of bits from the source encoder 104. Channel encoder 106 codesthe PCM digital signal using a channel code that has been constructed tomeet the design criteria elucidated below.

The code constructed for the second illustrative embodiment assumes thatthe number of antennas at the base station is two. The 4-PSK trelliscode with a transmission rate of 2 bits/sec/Hz is provided forillustrative purposes in FIG. 9. Using this code, encoder 106 codes twoinformation bits at a time to generate the label of a branch in thetrellis diagram. The branch depends on the state of the encoder and theinput data and determines the new state of the encoder as well. Forexample, suppose that the encoder is in state of FIG. 9. Then upon inputbits, 00, 01, 10, and 11, the respective branch labels are respectively30, 31, 32, and 33. The new state of the encoder is then respectively 0,1, 2, and 3. Each branch label comprises two symbols, (see branchlabels, above). Each symbol belongs to the 4-PSK constellation presentedin FIG. 4( a). Thus for instance corresponding to output 31, phasevalues 3π/2 and π/2 radians are used to phase modulate the carrier.Therefore, a coding rate of two information bits per channel used isprovided by this code. Symbol 1 is transmitted with antenna 116 a andsymbol 2 with antenna 116 b, as discussed below.

The first symbol of each codeword generated by encoder 106 is providedas input to constellation mapper 108 a, and the second symbol of thecodeword is provided to mapper 108 b, generally as discussed above forthe first illustrative embodiment.

K. Further Illustrative Channel Codes in Second Illustrative Embodiment

The second illustrative embodiment described above may employ otherchannel codes to enhance coding efficiency. These codes are designedaccording to a performance criteria computed later in the sequel. Forillustration, examples are provided. One can improve on the performanceof these codes by constructing encoders with more states. The inventorshave designed codes (using the criteria established) with differentnumbers of states. Simulation results for the case of 4-PSK and 8-PSKare included demonstrating that the performance of these codes for twoand one receive antenna is excellent.

L. Decoding in Second Illustrative Embodiment

The second illustrative embodiment makes use of receiver 300 and relateddecoder circuitry illustrated in FIG. 10, generally similar to thatshown in FIG. 5 described for the first illustrative embodiment. Asillustrated in FIG. 10, the circuitry constructed to receive symbolsfrom buffer 307 is adapted to account for the non-delayed coding of thesecond embodiment. For instance, since no delay is applied, the delayelement 315 shown in FIG. 6 is not incorporated when decoding accordingto the second illustrative embodiment.

M. Performance Criteria for Second Illustrative Embodiment

In this section, performance criteria for the design of the codes usedin the second illustrative embodiment are established.

Consider a mobile communication system such that the base station isequipped with n antennas and the mobile unit is equipped with mantennas. Data is encoded by the encoder. The encoded data goes througha serial to parallel device and is divided into n streams of data. Eachstream of data is used as the input to a pulse shaper. The output ofeach shaper is then modulated using a modulator. At each time the outputof modulator i is a signal that is transmitted using transmit antenna(Tx antenna) i for 1≦i≦n.

It is again assumed that the n signals are transmitted simultaneouslyeach from a different transmit antenna and that all these signals havethe same transmission period T. The signal at each receive antenna is anoisy version of the superposition of the faded version of the ntransmitted signals.

At the receiver, the demodulator makes a decision statistic based on thereceived signals at each receive antenna 1≦j≦m. Assuming that thetransmitted symbol from the i-th antenna at transmission interval t isc_(t) ^(i) the receive word at time interval t at the receive antenna jis d_(t) ^(j), then

$\begin{matrix}{d_{t}^{j} = {{\sum\limits_{i = 1}^{n}\;{\alpha_{i}^{j}c_{t}^{i}}} + \eta_{t}^{j}}} & (3)\end{matrix}$

The coefficients α_(i) ^(j) are first modeled as independent samples ofa stationary complex Gaussian stochastic process with mean Eα_(i)^(j)=p_(i) ^(j)+q_(i) ^(j) j and variance 0.5 per dimension with K_(i)^(j)=|E_(i) ^(j)|², where j=√{square root over (−1)}. Tis is equivalentto the assumption that signals transmitted from different antennasundergo independent fades (The case when α_(i) ^(j) are dependent willbe treated later). Also, η_(t) ^(j) are independent samples of a zeromean complex white Gaussian process with two sided power spectraldensity N₀/2 per dimension. It is assumed that α_(i) ^(j) are constantduring a frame and vary from one frame to another (flat fading).

The inventors have derived a design criterion for constructing codesunder this transmission scenario. Mathematical background required andthe notation used for this task is first reviewed. Let x=(x₁, x₂ . . . ,x_(k)) and (y₁, y₂, . . . , y_(k)) be complex vectors in the kdimensional complex space C^(k). The inner product x and y is given by

${{x \cdot y} = {\sum\limits_{i - 1}^{k}\;{x_{i}{\overset{\_}{y}}_{i}}}},$where ÿ_(i) denotes the complex conjugate of y_(i). For any matrix A,let A* denote the Hermitian (Transpose conjugate) of A.

From known linear algebra an n×n A is Hermitian if and only if A=A*. Ais non-negative definite if xAx*≧0 for any 1×n complex vector x. An n×nmatrix V is unitary if and only if VV*=I where I is the identity matrix.A n×1 matrix B is a square root of an n×n matrix A if BB*=A. Thefollowing results from linear algebra are also made use of.

-   -   An eigenvector v of an n×n matrix A corresponding to eigenvalue        λ is a 1×n vector of unit Euclidean length such that vA=λv for        some complex number λ. The number of eigenvectors of A        corresponding to the eigenvalue zero is n−r, where r is the rank        of A.    -   Any matrix A with a square root B is non-negative definite.    -   For any non-negative definite Hermitian matrix A, there exists a        lower triangular square matrix B such that BB*−=A.    -   Given a Hermitian matrix A, the eigenvectors of A span C^(n),        the complex space of n dimensions and it is easy to construct an        orthonormal basis of C^(n) consisting of eigenvectors A.    -   There exists a unitary matrix V and a real diagonal matrix D        such that VAV*=D. The rows of V are an orthonormal basis of        C^(n) given by eigenvectors of A.    -   The diagonal elements of D are the eigenvalues λ_(i), I=1, 2 . .        . , n of A counting multiplicities.    -   The eigenvalues of a Hermitian matrix are real.    -   The eigenvalues of a non-negative definite Hermitian matrix are        non-negative.

i. The Case of Independent Fade Coefficients

Assume that each element of signal constellation is contracted by ascale factor √{square root over (E)}, chosen so that the average energyof the constellation element is 1. Thus the design criterion is notconstellation dependent and applies equally to 4-PSK, 8-PSK and 16-QAM.

Consider the probability that the receiver decides erroneously in favorof a signale=e ₁ ¹ e ₁ ² . . . e ₁ ^(n) e ₂ ¹ e ₂ ² . . . e ₂ ^(n) . . . e ₁ ¹ e ₁² . . . e ₁ ^(n) assuming thatc=c ₁ ¹ c ₁ ² . . . c ₁ ^(n) c ₂ ¹ c ₂ ² . . . c ₂ ^(n) . . . c ₁ ¹ c ₁² . . . c ₁ ^(n) was transmitted.

Assuming ideal channel state information (CSI), the probability oftransmitting c and deciding in favor of e at the decoder is wellapproximate by

$\begin{matrix}{{{P( {  carrow e  \middle| \alpha_{i}^{j} ,{i = 1},2,\ldots\mspace{14mu},n,{j = 1},2,\ldots\mspace{14mu},m} )} \leq {\exp( {{- {d^{2}( {c,e} )}}{E_{s}/4}\; N_{0}} )}}\mspace{20mu}{where}} & (4) \\{\mspace{79mu}{{d^{2}( {c,e} )} = {\sum\limits_{j = 1}^{m}\;{\sum\limits_{t = 1}^{l}\;{{{\sum\limits_{i = 1}^{n}\;{\alpha_{i}^{j}( {c_{t}^{i} - e_{t}^{i}} )}}}^{2}.}}}}} & (5)\end{matrix}$

This is just the standard approximation to the Gaussian tail function.

Setting Ω_(j)=(α₁ ^(j), . . . , α_(n) ^(j)), (5) is rewritten as

$\begin{matrix}{{{d^{2}( {c,e} )} = {\sum\limits_{j = 1}^{m}\;{\Omega_{j}{A( {c,e} )}\Omega_{j}^{*}}}},} & (6)\end{matrix}$where the pq in element of A(c,e) is A_(pq)=x_(p)·x_(q) and x_(p)=(c₁^(p)−e₁ ^(p), c₂ ^(p)−e₂ ^(p), . . . , c₁ ^(p)−e₁ ^(p)) for 1≦p, q≦n.Thus,

$\begin{matrix}{{P( {  carrow e  \middle| \alpha_{i}^{j} ,{i = 1},2,\ldots\mspace{14mu},n,{j = 1},2,\ldots\mspace{14mu},m} )} \leq {\prod\limits_{j = 1}^{m}\;{{\exp( {{- \Omega_{j}}{A( {c,e} )}\Omega_{j}^{*}{E_{s}/4}\; N_{o}} )}.}}} & (7)\end{matrix}$

Since A(c,E) is Hermitian, there exists a unitary matrix V and a realdiagonal matrix D such that VA(c,e)V*=D. The rows of V are a completeorthonormal basis of C^(n) given by eigenvectors of A. Furthermore, thediagonal elements of D are the eigenvalues λ_(i)=1, 2, . . . , n of Acounting multiplicities. The matrix

$\begin{matrix}{{B( {c,e} )} = \begin{pmatrix}{e_{1}^{1} - c_{1}^{1}} & {e_{2}^{1} - c_{2}^{1}} & \ldots & {e_{1}^{1} - c_{1}^{1}} & \; \\{e_{1}^{2} - c_{1}^{2}} & {e_{2}^{2} - c_{2}^{2}} & \ldots & {e_{1}^{2} - c_{1}^{2}} & \; \\{e_{1}^{3} - c_{1}^{3}} & {e_{2}^{3} - c_{2}^{3}} & \ldots & {e_{1}^{3} - c_{1}^{3}} & 2 \\\vdots & \vdots & \ddots & \vdots & \; \\{e_{1}^{n} - c_{1}^{n}} & {e_{2}^{n} - c_{2}^{n}} & \ldots & {e_{1}^{n} - c_{1}^{n}} & \;\end{pmatrix}} & (8)\end{matrix}$is clearly a square root of A(c, e). Thus, the eigenvalues of A(c,e) arenon-negative real numbers.

Let ω_(j)=Ω_(j)V* and ω_(j)=(β₁ ^(j), . . . , β_(n) ^(j)), then

$\begin{matrix}{{\Omega_{j}{A( {c,e} )}\Omega_{j}^{*}} = {\sum\limits_{i = 1}^{n}\;{\lambda_{i}{\beta_{j}^{i}}^{2}}}} & (9)\end{matrix}$

Next, recall that α_(i) ^(j) are i.i.d. samples of a complex Gaussianprocess with mean Eα_(i) ^(j) with K_(i) ^(j)=|Eα_(i) ^(j)|². LetK^(j)=(Eα₁ ^(j), . . . , Eα_(n) ^(j), and let v_(w) denote the w-th rowof V.

Since V is unitary, (v₁, v₂, . . . , v_(n)) is an orthonormal basis ofc^(n) and β_(i) ^(j) are independent complex Gaussian random variableswith variance 0.5 per dimension and mean K^(j)·v_(i). LetK_(i,j)=|Eβ_(i) ^(j)|²=|K^(j)·v_(i)|². Thus |β_(i) ^(j)| are independentRician distributions with pdf p(|β_(i) ^(j)|)=2|β_(i) ^(j)|exp(−|β_(i)^(j)|²−K_(i,j))I₀(2|β_(i) ^(j)|√{square root over (K_(i,j))}), for|β_(i) ^(j)|≧0, where I₀(·) is the zero-order modified Bessel functionof the first kind.

Thus, to compute an upper bound on the average probability of error,simply average

$ {\prod\limits_{j = 1}^{m}\;{{\exp( {{E_{s}/4}N_{0}} )}{\prod\limits_{i = 1}^{n}\;{\lambda_{i}{\beta_{j}^{i}}^{2}}}}} )$with respect to independent Rician distributions of |β_(i) ^(j)| toarrive at

$\begin{matrix}{{P( carrow e )} \leq {\prod\limits_{j = 1}^{m}\;( {\prod\limits_{i = 1}^{n}\;{\frac{1}{1 + {\frac{E_{s}}{4\; N_{0}}\lambda_{i}}}{\exp( {- \frac{K_{i,j}\frac{E_{s}}{4\; N_{0}}\lambda_{i}}{1 + {\frac{E_{s}}{4\; N_{0}}\lambda_{i}}}} )}}} )}} & (10)\end{matrix}$

Some special cases are next examined.

The Case of Rayleigh Fading:

In this case K_(i) ^(j)=0 and as a fortiori K_(i,j)=0 for all i and j.Then the inequality (10) can be written as

$\begin{matrix}{{P( carrow e )} \leq {( \frac{1}{\prod\limits_{i = 1}^{n}\;( {1 + {\lambda_{i}{E_{s}/4}\; N_{0}}} )} )^{m}.}} & (11)\end{matrix}$

Let r denote the rank of matrix A, then the kernel of A has dimensionn−r and exactly n−r eigenvalues of A are zero. Say the nonzeroeigenvalues of A are λ₁, λ₂, . . . , λ_(r), then it follows frominequality (11) that

$\begin{matrix}{{P( carrow e )} \leq {( {\prod\limits_{i = 1}^{r}\;\lambda_{i}} )^{- m}{( {{E_{s}/4}\; N_{0}} )^{- {rm}}.}}} & (12)\end{matrix}$

Thus a diversity of mr and a gain of (λ₁, λ₂, . . . , λ_(r))^(1/r) isachieved. Recall that λ₁, λ₂, . . . , λ_(r) is the absolute value of thesum of determinants of all the principle r×r cofactors of A. Moreover,the ranks of A(c,e) and B(c,e) are equal. Thus from the above analysis,the following design criterion are arrived at.

Design Criteria For Rayleigh Space-Time Codes:

-   -   The Rank Criterion: In order to achieve the maximum diversity        mn, the matrix B(c,e) has to be full rank for any codewords c        and e. If B(c,e) has minimum rank r over the set of two tuples        of distinct codewords, then a diversity of rm is achieved.    -   The Determinant Criterion: Suppose that a diversity benefit of        rm is our target. The minimum of r-th roots of the sum of        determinants of all r×r principle cofactors of        A(c,e)=B(c,e)B*(c,e) taken over all pairs of distinct codewords        e and c corresponds to the coding gain, where r is the rank of        A(c,e). Special attention in the design must be paid to this        quantity for any codewords e and c. The design target is making        this sum as large as possible. If a diversity of nm is the        design target, then the minimum of the determinant of A(c,e)        taken over all pairs of distinct codewords e and c must be        maximized.

At sufficiently high signal to noise ratios, one can approximate theright hand side of inequality (10) by

$\begin{matrix}{{P( carrow e )} \leq {( \frac{E_{s}}{4\; N_{0}} )^{- {rm}}{{( {\prod\limits_{i = 1}^{r}\;\lambda_{i}} )^{- m}\lbrack {\prod\limits_{j = 1}^{m}\;{\prod\limits_{i = 1}^{r}\;{\exp( {- K_{i,j}} )}}} \rbrack}.}}} & (14)\end{matrix}$

Thus a diversity of rm and a gain of

${( {\lambda_{1}\lambda_{2}\ldots\mspace{14mu}\lambda_{r}} )^{1/r}\lbrack {\prod\limits_{j = 1}^{m}\;{\prod\limits_{i = 1}^{r}\;{\exp( {{- {Ki}},j} )}}} \rbrack}^{1/{rm}}$is achieved. Thus, the following design criteria is valid for the Ricianspace-time codes for large signal to noise ratios.

Design Criteria For Rician Space-Time Codes:

-   -   The Rank Criterion: This criterion is the same as that given for        the Rayleigh channel.    -   The Gain Criterion: Let A(c,e) denote the sum of all the        determinants of r×r principal co-factors of A(c,e), where r is        the rank of A(c,e). The minimum of the products

${{A( {c,e} )}^{1/r}\lbrack {\prod\limits_{j = 1}^{m}\;{\prod\limits_{i = 1}^{r}\;{\exp( {- K_{i,j}} )}}} \rbrack}^{1/{rm}}.$

-   -   Taken over distinct codewords c and e have to be maximized.    -   Note that it has been shown that, one could still use the gain        criterion f rte Rayleigh space-time codes as well, since the        performance will be at least as good as the right side of        inequality (11).

ii. The Case of Dependent Fade Coefficients:

Next, the case went e fade coefficients are dependent is studied. OnRayleigh fading is considered, as the Rician case can be treated in asimilar manner. To this end, consider the mn×mn matrix

${{Y( {c,e} )} = \begin{matrix}{A( {c,e} )} & 0 & \ldots & \ldots & 0 & 0 \\0 & {A( {c,e} )} & \ldots & \ldots & 0 & 0 \\0 & 0 & {a( {c,e} )} & \ddots & \vdots & 0 \\\vdots & \vdots & \ddots & \ddots & \vdots & \vdots \\0 & 0 & 0 & \ldots & 0 & {A( {c,e} )}\end{matrix}},$where 0 denote the all zero n×n matrix. Let Ω=(Ω₁, . . . , Ω_(m)), then(7) can be written asP(c→e|α _(i) ^(j) ,i=1,2, . . . n,j=1,2, . . . m)≦exp(−ΩY(c,e)Ω*E_(s)/4N ₀)  (15)

Let θ denote the correlation of Ω. Assume that θ is full rank (this is aphysically acceptable assumption). The matrix θ being a non-negativedefinite square Hermitian matrix has a full rank nm×nm lower triangularmatrix C as it's square root. The diagonal elements of θ are unity, sothat the rows of C arc of length one. Define v=(ε₁ ¹, . . . , ε_(n) ¹,ε₁ ², . . . , . . . ε₁ ^(m), . . . , ε_(n) ^(m)) by Ω=vC*, then it iseasy to see that the components of v are uncorrelated complex Gaussianrandom variables with variance 0.5 per dimension. The mean of thecomponents of v can be easily computed from the mean of α_(i) ^(j) andthe matrix C. In particular of the α_(i) ^(j) are of mean zero, so arethe ε_(i) ^(j).

By (15), the conclusion is arrived at thatP(c→e|α _(i) ^(j) ,i=1,2, . . . ,n,j=1,2, . . . ,m)≧(−γC*Y(c,e)Cγ*E_(s)/4N ₀).  (16)

The same argument can be followed as the case of independent fades withA(c,e) replaced by C*Y(c, e) C. It follows that the rank of C*Y(c,e) Chas to be maximized. Since C is full rank, this amounts to maximizingrank [Y(c,e)]=m rank [A(c,e)]. Thus the rank criterion given for theindependent fade coefficients holds in this case as well.

Since α_(i) ^(j) are zero mean, so are ε_(i) ^(j). Thus by a similarargument to that of the case of independent fade coefficients, theconclusion that the determinant of C*Y(c,e)C must be maximized isarrived at. This is equal to det (θ) det (Y(c,e))=det (θ) [det(A(c,e))]^(m). In this light the determinant criterion given in the caseof independent fade coefficients holds as well.

It follows from a similar argument that the rank criterion is also validfor the Rician case and that any code designed for Rician channelperforms well for Rayleigh channel even if the fade coefficients aredependent. To obtain the gain criterion, one has to compute the mean ofε_(i) ^(j) and apply the gain criterion given in the case of independentRician fade coefficients. As appreciated by persons skilled in the art,this is a straightforward but tedious computation.

N. Space-Time Code Construction

In this section, the results of the previous section are used to designcodes for a wireless communication system that employs n transmitantennas and (optional) receive antenna diversity, according to thesecond embodiment of the present invention.

The designed codes can be either trellis codes, or block codes having atrellis representation. Examples are provided of trellis codes, asgeneralization to block codes is straightforward, to persons skilled inthe art.

i. Trellis Codes

In the design of the codes to be applied in the second illustrativeembodiment, reference is made to those having the property that eachtransition branch at time t is labeled with a sequence q_(t) ¹q_(t) ² .. . q_(t) ^(n) of n symbols from the constellation alphabet Q for all1≦t≦1. Any time that the encoder's path goes through such a transitionbranch, the symbol q_(t) ¹ is sent via antenna I for all 1≦i≦n.

The encoding for trellis codes is straightforward, with the exceptionthat it is required that at the beginning and the end of each frame, theencoder be in known states. A method of decoding is illustrated next.Assuming channel estimates {circumflex over (α)}_(j) ^(i) of α_(i) ^(j),i=1,2, . . . , n, j=1,2, . . . , m are available to the decoder.Assuming that r_(t) ^(i) is the received signal at receive antenna i attime t, the decoder computes for any transition branch at time t havingthe label q_(t) ¹q_(t) ² . . . q_(t) ^(n), the branch metric

$\sum\limits_{j = 1}^{j}\;{{{r_{t}^{j} - {\sum\limits_{i = 1}^{n}\;{{\hat{\alpha}}_{i}^{j}q_{t}^{i}}}}}^{2}.}$

The Viterbi algorithm is then used to compute the path with lowestaccumulated metric.

The aforementioned trellis codes are called Space-Time codes, as theycombine spatial and temporal diversity techniques. Furthermore, if theSpace-Time code guarantee a diversity gain of rm for the multipleantenna communication systems discussed above, it is said that it is anr-Space-Time code.

A 4-state code for the 4-PSK constellation is given in FIG. 9. Forfurther illustration, there is also provided an 8-state code for the8-PSK constellation in FIG. 11, and 8, 16, and 32-state codes for the4-PSK constellation in FIGS. 12( a), 12(b), and 13, respectively. Alsoprovided is a 16-state code for 16-QAM constellation in FIG. 14.

The design rules that guarantee diversity for all the codes in FIGS. 11,12(a), 12(b), 13, and 14 are:

-   -   Transitions departing from the same state differ in the second        symbol.    -   Transitions arriving at the same state differ in the first        symbol.

r-space-times for r≧2:

As an illustration, a 4-space-time code for a 4 transmit antenna mobilecommunication systems is constructed. The input to the encoder is ablock of length 2 of binary numbers corresponding to an integer i inz₄=(0, 1, 2, 3). The states of the trellis correspond to set of allthree tuples (s1, s2, s3) with s_(i) in z₄, for 1<=i<=3. At state (s1,s2, s3) upon receipt of input data i, the encoder outputs (i, s₁, s₂,s₃) elements of 4-PSK constellation (see FIG. 4( a)) and moves to state(i, S₁, s₂). The performance of this code for 1 and 2 receive antennasis given in FIG. 15.

O. Channel Estimation and Interpolation

In both foregoing illustrated embodiments of the invention, it wasassumed that the channel state information which is needed for decodingis known. However, in reality the receiver must estimate the channelstate information. Also, the receiver must update this information asthe channel varies. As illustrated in FIG. 16, this may be accomplishedby the periodic transmission of a probe or pilot symbol p, whoseidentity is known at the transmitting and the receiving sides of thecommunication apparatus.

During the transmission of the pilot symbols, the receiver derivesestimate of the fade coefficients. The receiver estimates the channelstate over the whole frame of data using a channel interpolation scheme.The results of interpolation are used by the space-time decoder usingdecoding techniques known to the persons skilled in the art.

The inventors have observed that in high mobility environmentsinaccuracies in channel estimation and interpolation causes only a smallnumber of errors in frames of data output by the space-time decoder.These few errors can be corrected using any outer block codes as arewell-known in the art.

Her is described in implementation for a wireless modem that employs theuse of space-time codes according to the invention, along with a codingstrategy called concatenated space-time coding.

P. Basic Modem Architecture

In this section the basic functions of a modem based on space-time codedmodulation according to the invention are described. For the purpose ofillustration, the channelization of the North American digital cellularstandard IS-136 is assumed. However, the same modem architecture can beeasily adopted to other channelization and/or any other application withminor modifications know to people skilled in the art.

A brief overview of the frame structure in IS-136 is as follows. On each30 kHz wireless channel, the IS-136 standard defines 25 frames of dataper second, each of which is then further subdivided into 6 time slots.Each time slot is of a 6.667 ms duration and carries 162 modulationsymbols (modulation symbol rate is 24,300 symbols/sec).

i). Transmitter

FIG. 17 shows a block diagram for a transmitter that employs space-timecoding and is equipped with 2 transmit antennas (the extension of thesame architecture to more than 2 transmit antennas is straightforward).A bit stream from the information source (either speech or data) is fedto the space-time encoder. The space-time encoder groups each binformation bits into one modulation symbol, where the number of bits bper modulation symbols will depend on the constellation used, which isassumed to be either M-QAM or M-PSK constellation. Te space-time encoderuses a space-time code constructed according to criterion mentionedabove.

Each group of b information bits generates two modulation symbols at theoutput of the space-time encoder. Each stream of modulation symbols isinterleaved using a block interleaver. It is assumed that both burstsare interleaved in a similar way. Overhead, synchronization, and pilotsymbols are then added to the output of each interleaver to build aburst. Each burst is then pulse-shaped using any suitable pulse shapeknown to persons skilled in the art, and transmitted from itscorresponding antenna.

ii). Time Slot Structure

For the purpose of illustration, FIG. 16 shows a slot structure for thecase when the transmitter is equipped with two transmit antennas andfollows IS-136 channelization. As mentioned, this slot structure can beeasily extended to conform to other channelization and any number oftransmit antennas.

In each time slot, two bursts are transmitted, one from each antenna. Asin IS-136 North American Digital Cellular Standard, it is assumed thatthe modulation symbol rate is 24,300 symbols/sec and each burst consistsof 162 symbols. Each burst starts with a 14 symbol synchronizationsequence S₁ and S₂ that is used for timing and frequency synchronizationat the receiver. In addition, the transmitter inserts 6 two-symbol pilotsequences P₁ and P₂ that will be used at the receiver to estimate thechannel. The signal received at the receiver is the superposition of thetwo transmitted bursts, and in order to separate the two bursts at thereceiver, it is necessary to define the two sequences S₁ and S₂ as wellas the pilot sequences P₁ and P₂ as orthogonal sequences. It is assumedthat the synchronization and pilot symbols have the same energy persymbol as the information symbols. In addition, for the synchronizationand pilot sequences π/4-shifted DQPSK modulation is used. Each burstwill then have 136 symbols of information. The block interleaver will bethen a 17×8 block interleaver.

iii). Receiver

FIG. 18 shows the corresponding block diagram for a mobile receiverequipped with two receive antennas according to this embodiment. Foreach receiver antenna, after matched filtering, the receiver splits theoutput samples into two streams.

The first stream contains the received samples that correspond to theinformation symbols. The second stream contains the received samplescorresponding to the pilot symbols. These samples are first correlatedwith the pilot sequence for bursts transmitted from transmit antenna 1to get an estimate for the channel (at the pilot positions) fromtransmit antenna 1 to the corresponding receive antenna. Also, the sameset of samples are correlated with the pilot sequence for burststransmitted from transmit antenna 2 to get an estimate for the channel(at the pilot positions) from transmit antenna 2 to the correspondingreceive antenna. These estimates are then interpolated to form anestimate for channel state information needed for maximum likelihooddecoding according to the metric previously defined. The interpolationfilter can be designed in many ways known to persons skilled in the art.For optimum interpolation, a different interpolation filter should beused for every value of Doppler spread f_(d), frequency offset f_(o),and signal to noise ratio SNR. However, this approach will be of greatcomplexity for any practical implementation. Various approaches areproposed ere. The first is to use a robust filter that will cover allpossible range of operation, although this will lead to a slightdegradation in performance at low Doppler and/or frequency offsetvalues.

The second approach is to divide the range of operation into differentregions, and for every region design an optimum interpolator for someoperating point in that region and use that filter for the whole. Byobserving the channel correlation from the channel estimates or byobserving the symbol error rate, the receiver can decide which filter touse for interpolation.

In addition, in estimating the channel over any burst, the pilot symbolsin that burst are only used. This will minimize the overall system delayby avoiding the need to wait for future bursts in order to estimate thechannel. Both data streams are then deinterleaved and fed to a vectorViterbi decoder.

iv). Basic Modem Performance

In this section, simulation results for the basic modem and time slotstructure described above are presented. In addition, the pulse shapethat was used is a square-root raised-cosine Nyquist pulse with roll-offfactor of 0.35. At the receiver an oversampling factor of 8 is assumed.

FIG. 19 shows the frame error rate (FER) P_(F) performance of the abovemodem for different values of Doppler spread f_(d) assuming perfecttiming and frequency synchronization. For the static case, perfectknowledge of the CSI for comparison, is assumed. Plotted is P_(F) versusSNR (or symbol energy to noise ratio) E_(S)/N₀. For the ideal CSI, itcan be seen that a FER of 0.1 at E_(S)/N₀ of 14.75 dB. However, for aDoppler spread f_(d) of 170 Hz, which corresponds to a vehicle speed of60 mph, the 0.1 FER is achieved t 20.5 dB E_(S)/N₀. For f_(d)=120 Hz,this number drops to 17.1 dB. It can also be noticed that FER floors athigh E_(S)/N₀. In general, this increase in the required E_(S)/N₀ ascompared to the case with ideal CSI and the FER flooring are due to theerrors in channel estimation.

Q. Third Illustrative Embodiment-Concatenated Space-Time Coding

FIG. 20 shows the distribution of the number of symbol errors per framefor the f_(d)=170 Hz for different values of E_(S)/N₀. For relativelyhigh values of E_(S)/N₀ (>15 dB), approximately 90% of the frames thatare in error, the error is due to 5 symbol errors or less. Most of theseerrors can be recovered from, by concatenating the space-time code withany block code known to the persons skilled in the art, such as a ReedSolomon (RS) code. This overall coding strategy is designatedconcatenated space-time coding and is shown in FIGS. 21 and 22.Depending on the desired error correction capability and rate of thecode and the type of constellation used, the dimension of the block codeused should be such to produce an integer multiple of modulation symbolsfor each RS symbol. In this way, it will be possible to decode a burseimmediately without the need to wait for other bursts and, thereby,minimize decoding delay. In addition, in this way, any symbol error atthe output of the ST decoder will affect only one RS code symbol.

R. Modem Performance with Concatenated Space-Time Coding

The inventors simulated the above-described modem with the space-timecode concatenated with a Reed-Solomon code. Three different shortened RScodes over GF(2⁸) symbols are first created by partitioning the bitstream into 66 groups of 8 bits each. The output 68 GF(2⁸) symbols arethen partitioned into 136 16-QAM symbols, 2 channel symbols per oneReed-Solomon code, referred to as RS3, is a shortened (68, 62) code thatcorrects three byte errors, and the third code, referred to as RS5, is ashortened (68,58) code that corrects 6 byte errors. In this simulation,a timing error of ±T/16 and a frequency offset f_(o) of 200 Hz areassumed.

FIG. 23 shows the FER performance with concatenated space-time codingand in the presence of timing error and frequency offset for f_(d)=170Hz. From this figure, it can be seen that in the case of the ST codealone a E_(S)/N₀ of 23 dB is required to achieve P_(F) of 0.1. However,when the ST code is concatenated with RS3, for example, the requiredE_(S)/N₀ is 17.5 dB, i.e., a 5.5 dB gain over the ST code alone.However, in this case, the net bit rate (per 30 kHz channel) will bereduced from 81.6 kbits/sec to 74.4 kbits/sec. If RS5 is used, therequired E_(S)/N₀ for P_(F)=0.1 will drop to 16.5 dB, which is only 1.75dB higher than the case when ideal CSI are available. In this case, thenet bit rate will be 69.6 kbits/sec.

S. Fourth Illustrative Embodiment-Multi Level Structured Space TimeCodes

Some of the space-time codes described in the second embodiment of thisinvention may have multilevel structure. On occasions, it may bedesirable to take advantage of this structure in practical communicationsystems, particularly when the number of transmit antennas is high. Thishas the significant advantage of reducing decoding complexity.Multilevel code structures and associated decoding techniques are knownin the art. They can be combined with space-time coding, giving rise tothe invention of a novel technique called multi-level space-time coding.

Without loss of generality, assume that the signal constellation Q₀consists of 2^(b) ⁰ points. Assume that f-levels of coding is used.Associated with this f-levels of coding, a partition based on subsetsQ _(f−1) ⊂Q _(f−2) ⊂ . . . Q ₁ ⊂Q ₀is chosen with the number of elements of Q_(j) equal to 2^(b) ^(j) forall 0≦j≦f−1. By such a partitioning, it is meant that Q₀ is the union2^(b) ⁰ ^(−b) ¹ disjoint sets called cosets of Q₁ in Q₀, each having2^(b) ¹ elements such that one of these cosets is Q₁. Having the cosetsof Q₁ in Q₀ at hand, each coset is then divided into 2^(b) ¹ ^(−b) ²disjoint sets each having 2^(b) ² elements. The 2^(b) ¹ ^(−b) ² subsetsof Q₁ are called cosets of Q₂ in Q₁. The set of cosets of Q₂ in Q₁ mustinclude Q₂. Thus there are 2^(b) ⁰ ^(−b) ² subsets of Q₀ with 2^(b) ²elements called the cosets of Q₂ in Q₀. The set of cosets of Q₂ in Q₀includes Q₂. This procedure is repeated until cosets of Q_(j) in Q_(k)for all 0≦k<j≦f−1 are arrived at. Let r_(f−1)=b_(f−1) andr_(j)=b_(j+1)−b_(j) for j=0, 1, . . . f−2. Then Q_(j) contains 2^(r)^(j) cosets of Q_(j+1) for all j=0, 1, . . . , f−2.

Every K=K₀+ . . . +K_(f−1) bits of input data is encoded using encoders0,1, . . . , f−1 corresponding to the f levels. It is required that allthe encoders have a trellis representation. At each time t depending onthe state of the j-th encoder and the input data, a branch of thetrellis of the j-th encoder is chosen which is labeled with n blocks ofr_(j) bits denoted by B_(t) ^(i)(j), B_(t) ²(j), . . . , B_(t) ^(n)(j).The blocks B_(t) ^(i)(0), . . . , B_(t) ^(i)(f−1) then choose a point ofthe signal constellation in the following way.

The block B_(t) ^(i)(0) chooses a coset Q₁′ of Q₁ in Q₀. The block B_(t)^(i)(1) chooses a coset Q₂′ of Q₂ in Q₁ and so forth. Finally, the blockB_(t) ^(i)(f−1) chooses a point Q_(f−1)′ of a coset of Q^(f−1) a chosenin the last step. The chosen point is then transmitted using the i-thantenna for 1≦i≦n. Multilevel decoding can be done in a manner known tothose skilled in the art.

Suppose that the encoder of the j-th level has 2^(S) ^(j) states at timet. One can view the multi-level code described above as a space-timecode C with 2^((S) ⁰ ^(+ . . . +S) ^(f−1) ⁾ states at time t. The statesof C correspond f-tuples (s_(t) ⁰, s_(t) ¹, . . . , s_(t) ^(f−1)) ofstates of encoders 0,1, . . . , f−1. The branch labels between states(s_(t) ⁰, s_(t) ¹, . . . , s_(t) ^(f−1)) and (s_(t+1) ⁰, s_(t+1) ¹, . .. , s_(t+1) ^(f−1)) is the set of symbols that are sent via antennas 1,2, . . . n if each encoder j goes from states s_(t) ^(j) for 0≦j≦f−1. Inthis way, one can view a multi-level space-time code as a regularspace-time code with a multi-level structure that allows simplifieddecoding. The penalty for this simplified decoding is loss inperformance. Also, the design criterion derived previously could beapplied to the space-time code C. Alternatively the design criteria caninstead by applied to the trellis of each encoder 0≦j≦f−1 providingdifferent diversities at each level.

The discussion of the illustrative embodiment above is illustrated withan example. Consider the transmission of 4-bits/sec/HZ using the 16-QAMconstellation and the set partitioning of FIG. 24. At each time inputbits are grouped into two blocks of two bits. The first and secondblocks of two bits input data are respectively the input to the firstand second encoder whose trellis is given in FIG. 25. Each branch of thetrellis is labeled with two blocks of two bits of data. These two bitsare represented with numbers 0, 1, 2 and 3. Upon the choice of brancheswith respective labels a₁a₂ and b₁b₂ by the zero-th and the firstencoders, the signal points 4a₁+b₁ and 4a₂+b₂ are sent via antennas 1and 2. The equivalent 16-state space-time trellis code is given in FIG.26.

T. Fifth Illustrative Embodiment: Smart-Greedy Codes

Smart greedy codes are a class of space-time codes of particularinterest in the implementation of the invention. These codes are able totake special advantage of possible rapid changes in the channel withoutany feedback from the receiver. The idea is to construct codes using ahybrid criteria such that possible rapid changes in the channel is takeninto account by the design criteria. In this light, an analysis isprovided for the case of rapidly fading channels as well.

i) Analysis of Rapid Fading

In this connection, the model of a mobile communication system having nantennas at the base and m antennas at the mobile station is refined.Data is encoded using a channel code. As in other embodiments, theencoded data goes through a serial to parallel device and is dividedinto n streams of data. Each stream of data is used as the input to apulse shaper. The output of each shaper is then modulated using amodulator. At each time the output of modulator I is a signal that istransmitted using transmit antenna (Tx antenna) I for 1≦i≦n. Again, then signals are transmitted simultaneously each from a different transmitantenna and all these signals have the same transmission period T. Thesignal at each receive antenna is a noisy version of the superpositionof the faded versions of the n transmitted signals. Assume that eachelement of the signal constellation is contracted by a scale factor√{square root over (E_(s))} chose so that the average energy of theconstellation is 1.

At the receiver, the demodulator makes decision statistic based on thereceived signals at each receive antenna 1≦j≦m. Let c_(t) ^(i) denotethe transmitted symbol from the i-th transmit antenna at transmissioninterval t and d_(t) ^(j) be the receive word at the receive antenna j.Then,

$\begin{matrix}{\mspace{79mu}{d_{t}^{j} = {{\sum\limits_{i = 1}^{n}\;{{\alpha_{i}^{j}(t)}c_{t}^{i}\sqrt{E_{s}}}} + \eta_{t}}}} & (18)\end{matrix}$This is equivalent to the assumption that signals transmitted fromdifferent antennas undergo independent fades. The coefficients ∝_(i)^(j)(t) are modeled as samples of a stationary complex Gaussianstochastic process with mean zero and variance 0.5 per dimension. Also,η_(i) ^(j) are independent samples of a zero mean complex white Gaussianprocess with two sided power spectral density N₀/2 per dimension. Forthe static fading case, support that ∝_(i) ^(j)(t) are constant during aframe and are independent from one frame to another and a designcriterion was established. When the fading is rapid, the coefficients∝_(i) ^(j)(t),t+1,2, . . . , 1,i=1,2, . . . , n,j=1,2, . . . , m aremodeled as independent samples of a complex Gaussian process with meanzero and variance 0.5 per dimension, and another design criteria isestablished as follows.

Assuming that the coefficients ∝_(i) ^(j)(t) for t=1,2, . . . , 1,i=1,2,. . . , n,j=1,2, . . . , m are known to the decoder, the probability oftransmittingc=c ₁ ¹ c ₁ ² . . . c ₁ ^(n) c ₂ ¹ c ₂ ² . . . c ₂ ^(n) . . . c ₁ ¹ c ₁² . . . c ₁ ^(n),and deciding in favor ofe=e ₁ ¹ e ₁ ² . . . e ₁ ^(n) e ₂ ¹ e ₂ ² . . . e ₂ ^(n) . . . e ₁ ¹ e ₁² . . . e ₁ ^(n)at the decoder is well approximated byP(c→e|α _(i) ^(j) ,i=1,2 . . . ,n,j=1,2, . . . ,m,t=1,2, . . .,l)≦exp(−d ²(c, e)E _(s)/4N ₀)where

$\begin{matrix}{{d^{2}( {c,e} )} = {\sum\limits_{j = 1}^{m}\;{\sum\limits_{t = 1}^{l}\mspace{11mu}{{\sum\limits_{i = 1}^{n}{{\alpha_{i}^{j}(t)}( {c_{t}^{i} - e_{t}^{i}} )}}}^{2}}}} & (19)\end{matrix}$This is the standard approximation to the Gaussian tail function.

LetΩ_(j)(t)=(α₁ ^(j)(t),α₂ ^(j)(t), . . . ,α_(n) ^(j)(t))and C(t) denote the n×n matrix with the element at p-th row and q-thcolumn equal to (c_(t) ^(p)−e_(t) ^(p))(ē_(t) ^(q)−ē_(t) ^(q)). The itcan be seen that

$\begin{matrix}{{d^{2}( {c,e} )} = {\sum\limits_{j = 1}^{m}\;{\sum\limits_{t = 1}^{l}{{\Omega_{j}(t)}{C(t)}{\Omega_{j}^{*}(t)}}}}} & (20)\end{matrix}$The matrix C(t) is Hermitian, thus there exist a unitary matrix V(t) anda diagonal matrix D(t) such that C(t)=V(t)D(t)V*(t). the diagonalelements of D(t), denoted here by D_(ii)(t),1≦i≦n, are the eigenvaluesof C(t) counting multiplicities. Such C(t) is Hermitian, theseeigenvalues are real numbers. LetΛ_(j)(t)=Ω_(j)(t)V(t)=(λ₁ ^(j)(t), . . . ,λ_(n) ^(j)(t)),then λ_(i) ^(j)(t) for i=1,2, . . . , n,j=1,2, . . . , m,t=1,2, . . . ,1 are independent complex Gaussian variables with mean zero and variance0.5 per dimension and

${{\Omega_{j}(t)}{C(t)}{\Omega_{j}^{*}(t)}} = {\sum\limits_{i = 1}^{n}{{{\lambda_{i}^{j}(t)}}^{2}{{D_{i\; i}(t)}.}}}$By combining this with (19) and (20) and averaging with respect to theRayleigh distribution of |λ_(i) ^(j)(t)|, the following is arrived at

$\begin{matrix}{{P( carrow e )} \leq {\prod\limits_{i,t}\;{( {1 + {{D_{ii}(t)}\frac{E_{s}}{4\; N_{0}}}} )^{- m}.}}} & (21)\end{matrix}$The matrix C(t) is next examined. The columns of C(t) are all differentmultiples ofc ₁ −e ₁=(c ₁ ¹ −e _(t) ¹ ,c _(t) ² −e _(t) ² , . . . ,c ₁ ^(n) −e ₁^(n)).

Thus, C(t) has rank 1 if c_(t) ¹c_(t) ² . . . c_(t) ^(n)≠e_(t) ¹ e _(t)² . . . e_(t) ^(n) and rank zero otherwise. It follows that n−1 elementsin the listD ₁₁(t),D ₂₂(t), . . . ,D _(nn)(t)Are zeros and the only possible nonzero element in this list is|c_(t)−e_(t)|². By (21), it can be concluded that

$\begin{matrix}{{P( carrow e )} \leq {\prod\limits_{t = 1}^{l}\;( {1 + {{{c_{t} - e_{t}}}\frac{E_{s}}{4\; N_{0}}}} )^{- m}}} & (22)\end{matrix}$Let V(c,e) denote the set of time instances 1≦t≦1 such that|c_(t)−e_(t)|≠0 and let |V(c,e)| denote the number of elements ofv(c,e). Then it follows from (22) that

$\begin{matrix}{\mspace{79mu}{{P( carrow e )} \leq {\prod\limits_{t \in {v{({c,e})}}}{( {{{c_{t} - e_{t}}}2\frac{E_{s}}{4\; N_{0}}} )^{- m}.}}}} & (23)\end{matrix}$It follows that a diversity of m|V(c,e)| is achieved. Examining thecoefficient of (E_(s)/4N_(o))^(−mV(c,e)) leads to the desired designcriterion. Below, this criterion is combined with that of static flatfading case given before to arrive at a hybrid criteria.

U. A Hybrid Design Criteria for Smart Greedy Space-Time Codes:

The Distance/Rank Criterion:

In order to achieve the diversity nm in a rapid fading environment, forany two code words c and e the strings c_(t) ¹c_(t) ² . . . c_(t) ^(n)and e_(t) ¹e_(t) ² . . . e_(t) ^(n) must be different at least for nvalues of 1≦t≦n. Furthermore, let

${B( {c,e} )} = \begin{pmatrix}{e_{1}^{1} - c_{1}^{1}} & {e_{2}^{1} - c_{2}^{1}} & \ldots & {e_{t}^{1} - c_{t}^{1}} \\{e_{1}^{2} - c_{1}^{2}} & {e_{2}^{2} - c_{2}^{2}} & \ldots & {e_{t}^{2} - c_{t}^{2}} \\{e_{1}^{3} - c_{1}^{3}} & {e_{2}^{3} - c_{2}^{3}} & \ddots & {e_{t}^{3} - c_{t}^{3}} \\\vdots & \vdots & \ddots & \vdots \\{e_{1}^{n} - c_{1}^{n}} & {e_{2}^{n} - c_{2}^{n}} & \ldots & {e_{t}^{n} - c_{t}^{n}}\end{pmatrix}$If B(c,e) has minimum rank r over the set of pairs of distinct codeword,then a diversity of rm is achieved in static flat fading environments.

The Product/Determinant Criterion:

Let V(c,e) denote the set of time instances 1≦t≦1 such that c_(t) ¹c_(t)² . . . c_(t) ^(n)≠e_(t) ² . . . e_(t) ^(n) and let

${{c_{t} - e_{t}}}^{2} = {\sum\limits_{i = 1}^{n}{{( {c_{t}^{i} - e_{t}^{i}} )}^{2}.}}$Then to achieve the most coding gain in a rapid fading environment, theminimum of the products Π_(tεv(c,e))|c_(t)−e_(t)|² taken over distinctcodewords e and c must be maximized. For the case of a static fadingchannel, the minimum of r-th roots of the sum of determinants of all r×rprincipal cofactors of A(c,e)=B(c,e)B*(c,e) taken over all pairs ofdistinct codewords e and c corresponds to the coding gain, where r isthe rank of A(c,e).

The construction of illustrative implementations of smart greedy codesaccording to this embodiment of the invention is illustrated with someexamples. It will be assumed that at the beginning and the end of theframe, the encoder is in the zero state.

Example A

Suppose that a transmission rate of 0.5 bits/sec/Hz is required. In thisexample and as illustrated in FIG. 27( a), the BPSK constellation isused, with 0 denoting √{square root over (E_(s))} and 1 denoting−√{square root over (E_(s))}. The objective is to guarantee diversitygains 2 and 4 respectively in slow and rapid flat fading environments.The following code using M-TCM construction guarantees these diversitygains. At any time 2K+1,k=0, 1, 2, . . . depending on the state of theencoder and the input bit a branch is chosen by the encoder and thefirst coordinate and second coordinates of the labels are sentsimultaneously from Tx antennas at times 2k+1 and 2K+2. For instance attime 1, if the branch label 10 11 is chosen, symbols 1,0 and 1,1 aresent respectively from transmit antennas one and two at times one andtwo.

Example B

Here a transmission rate of 1 bits/secs/Hz and diversity gains of 2 and3 respectively in static and rapid flat fading environments are desired.In this example, illustrated in FIG. 27( b), the 4-PSK constellation isused instead. The objective is to guarantee diversity gains 2 and 3respectively in slow and rapid flat fading environments. The followingcode using M-TCM construction guarantees these diversity gains. At timest=3k,k=0,1,2, . . . , three bits of data arrive at the encoder. Thefirst bit choose a branch depending on the state of the encoder and therest of two bits choose one of the 4 labels of that branch such as b_(t)¹b_(t) ²b_(t+1) ¹b_(t+1) ²b_(t+2) ¹b_(t+2) ². Then b_(t) ¹, b_(t+1) ²and b_(t+2) ¹ are sent via antenna 1 respectively at times t, t+1 andt+2. Similarly, b_(t) ², b_(t+1) ² and b_(t+2) ² are sent via antenna 2respectively at time t, t+1 and t+2.

As before, the inventors have simulated the performance of communicationsystems designed based on the above code. Excellent results have beenconfirmed in both fast and slow fading environments.

The foregoing description of the system and method of the invention isillustrative, and variations in construction and implementation willoccur to persons skilled in the art. For example, although the presentinvention is described in the time domain, frequency domain analogs orvariants of it easily occur to those skilled in the art. For instance,space-time codes presented in the second illustrative embodiment can beeasily applied to DS-CDMA communication systems. To illustrate, assumethat user X is provided with two transmit antennas (with generalizationto n antennas being trivial to those skilled in the art). User X choosesa space-time code designed to be used with two transmit antennas. User Xcan use a similar PN sequence for data transmission from both antennas.At the receiver side, correlation with the aforementioned sequence givesa sum of faded versions of the signals transmitted from each antenna. Inthis light, decoding of the space-time code can be carried out in amanner similar to those described in the second embodiment of this workas well.

Alternatively, user X can use distinct PN sequences for transmissionfrom both transmit antennas. If the PN sequences used to transmit fromboth antennas are orthogonal to each other, at the receiver co-relationwith the first or second sequence gives respectively noisy versions ofthe transmitted signals from antennas one or two, which can be used fordecoding at the receiver. This has a penalty in terms of bandwidthexpansion but can be used to increase the data rate and/or providediversity advantage.

In general, it is also possible to choose two arbitrary PN sequences fortwo transmit antennas. Correlation with these sequences at the receiverside gives sums of faded versions of multiples of the transmittedsignals that can be used for decoding.

The above discussion demonstrates a DS-CDMA analog of the space-timecoding. Analogs of the embodiments of the present invention in frequencydomain also can easily be obtained, but are not discussed here.

For further instance, while mobile cellular implementations have beendescribed, the invention could be applied to other communicationenvironments. The invention is accordingly intended to be limited onlyby the following claims.

What is claimed:
 1. An encoder, comprising: a processor configured to:employ a code structure with branches where the branches of the codestructure have labels that correspond to sets comprising of n symbolsthat are elements of a signal constellation; select a branch of the codestructure based on input data, and a previous state of the encoder; andtransmit a set of the sets of n symbols of the signal constellation thatcorresponds to a branch label of the branch that is selected, over aplurality of n antennas simultaneously.
 2. The encoder of claim 1,wherein the branch is selected by selecting, at each time t, branches ofa form q_(t) ¹q_(t) ² . . . q_(t) ^(n).
 3. The encoder of claim 1,wherein the encoder transmits using phase shifts of a carrier.
 4. Theencoder of claim 1, wherein the encoder delays a transmission of atleast one symbol by a predetermined time delay.
 5. The encoder of claim1, wherein the code structure comprises a space-time code.
 6. Theencoder of claim 1, wherein the encoder converts each of the n symbolsinto baseband signals and multiplies each of the baseband signals by aselected, respective, PN bit sequence.
 7. The encoder of claim 6,wherein a first of the respective PN bit sequence is the same as asecond of the respective PN bit sequence.
 8. The encoder of claim 6,wherein a first of the respective PN bit sequence is correlated to asecond of the respective PN bit sequence.
 9. A method of encoding,comprising: employing a code structure with branches where the branchesof the code structure have labels that correspond to sets comprising ofn symbols that are elements of a signal constellation; selecting, by aprocessor, a branch of the code structure based on input data, and aprevious state of an encoder; and transmitting a set of the sets of nsymbols of the signal constellation that corresponds to a branch labelof the branch that is selected, over a plurality of n antennassimultaneously.
 10. The method of claim 9, wherein the branch isselected by selecting, at each time t, branches of a form q_(t) ¹q_(t) ². . . q_(t) ^(n).
 11. The method of claim 9, wherein the transmittinguses phase shifts of a carrier.
 12. The method of claim 9, wherein thetransmitting delays a transmission of at least one symbol by apredetermined time delay.
 13. The method of claim 9, wherein the codestructure comprises a space-time code.
 14. The method of claim 9,further comprising: converting each of the n symbols into basebandsignals and multiplies each of the baseband signals by a selected,respective, PN bit sequence.
 15. The method of claim 14, wherein a firstof the respective PN bit sequence is the same as a second of therespective PN bit sequence.
 16. The method of claim 14, wherein a firstof the respective PN bit sequence is correlated to a second of therespective PN bit sequence.
 17. A transmitter for transmitting a digitalsignal comprising: n antennas; a module that provides a signal to the nantennas and which employs a multi-level structured space-time code withan encoder at each level having a code structure, wherein the moduleselects branches of the code structure at different levels, and selectsconstellation points of a constellation based on labels of the branchesthat are selected and a set partitioning of the constellation, with theconstellation points corresponding to the labels of the branches beingtransmitted over the n antennas simultaneously.
 18. The transmitter ofclaim 17, wherein: the module selects the branches of the codestructure, at each time t, branches of a form q_(t) ¹q_(t) ² . . . q_(t)^(n).